Problem: $f(x) = 2x^{2}-1$ What is the range of $f(x)$ ?
Answer: Consider the range of $2x^{2}$ The range of $x^2$ is $\{\, y \mid y \ge 0 \,\}$ Multiplying by $2$ doesn't change the range. To get $2x^{2}-1$, we subtract $1$. So the range becomes: $\{\, y \mid y ≥ -1 \,\}$.